Evolutionsgleichungen in Banach-Räumen

Ohne ZusammenfassungAus dem Institut für Angewandte Mathematik, Heidelberg     

Two-nucleon transfer reactions in deformed nuclei using very heavy ions

Semiclassical methods found to be highly accurate for inelastic scattering are applied to the calculation of rotational population signatures in heavy-ion two-neutron transfer reactions involving highly deformed targets. Basic features to be expected for such reactions are predicted, and are shown to have straightforward semiclassical interpretations. The rotational population signatures for 2-neutron transfer are shown to be quite different from those expected for the analogous inelastic scattering case. Several calculations are shown for Xe projectiles on rare-earth targets, and it is demonstrated that such reactions can provide a unique probe of nuclear structure in high angular momentum states. The extension of the general ideas employed here to 1-nucleon transfer in deformed nuclei and to several other examples of transfer to highly collective states in deformed and vibrational nuclei using very heavy ions is briefly considered. Experimental possibilities are discussed, and it is concluded that relevant experiments in this virtually unexplored area are possible using sophisticated particle-γ spectroscopic techniques.     

Application of a Bäcklund transformation in gravity driven two phase filtration

A nonlinear boundary value/initial value problem in two-phase filtration under gravity is solved analytically via the application of two successive Bäcklund transformations.     

Observation of pure quadrupole resonance in zinc metal

We report the first observation of nuclear quadrupole resonance (NQR) in Zn metal. A resonance line, which under the assumption of axial symmetry (η=0) corresponds to the $\text{|M| =}\text{3}\text{2}\text{?}\text{5}\text{2}$ transition in the $\text{I =}\text{5}\text{2}$ ground state of ⁶⁷Zn, has been found at v = 4.086(2) MHz at 4.2K. This yields (for η=0) a quadrupole coupling constant of $\text{e}{}^2\text{qQ}\text{h}\text{= 13.620(8)}$MHz, which is the most accurate value currently available.     

Gamma and Alpha decay from the 2.1-msec isomer213mRa

The isomer^213mRa was produced by the reaction²⁰⁹Bi(¹⁰B, 6n), as well as by bombardments of¹²C on Pb isotopes,¹⁴N on Bi, and¹⁶O on natural Hg, with projectile energies in the range 60–100 MeV. The isomer decays with a halflife of 2.1 ms both via gamma internal transitions and via alpha branching to levels in²⁰⁹Rn. A level scheme is proposed in which the isomeric state is assigned as either 17/2^– or 13/2⁺ with shell-model configurations either of theh _9/2 protons coupled to ap _1/2 neutron hole, or of an uncoupledi _13/2 neutron hole. On the basis of alpha decay rate predictions from the new Fliessbach theory, the 17/2^– isomeric assignment is to be preferred.Phys. Abstracts classifications 4.200–4.375     

Pion condensation and the σ-model in liquid neutron matter

The nature of the ground state of neutron matter at neutron star densities is discussed, starting from the linear σ-model Lagrangian. It is found that there is a possibility of a new, previously unknown, type of condensation, which involves coherent, non-vanishing expectation values of the neutral meson fields of the theory, the σ and π⁰ fields. The σπ⁰ condensate would, like normal neutron matter, develop its own π^? condensate. It is shown that the most general, translationally invariant, condensate is a combined σπ⁰ and π^? condensate with arbitrary, independent, wave numbers. The wave vectors of the condensates are determined by a minimization process, and are found to be non-vanishing and perpendicular.The σπ⁰ condensate corresponds to a state which is very different than previously considered states of neutron matter: all neutron spins are aligned, presumably with some macroscopic domain structure. Thus, criteria for the occurence of this condensate depend on the energy difference between very different states. This means that any prediction as to whether or not the state actually occurs in nature must at the moment be regarded as uncertain. However, using available hyperneted-chain calculations of the contribution to the energies from the direct neutron-neutron forces, it is demonstrated that a σπ⁰ condensate (with its accompanying π^? condensate) might well occur at neutron densities above perhaps 0.5 particles/fm³.This paper leans heavily on the linear σ-model. However, the neutral condensate is a general consequence of chiral symmetry, and can thus also be obtained e.g. from Weinberg's Lagrangian.     

Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning

The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students’ mathematical progress.